This automation industry quiz question comes from the ISA Certified Control Systems Technician (CCST) program. Certified Control System Technicians calibrate, document, troubleshoot, and repair/replace instrumentation for systems that measure and control level, temperature, pressure, flow, and other process variables. Click this link for more information about the CCST program.
A fluid is flowing through a 10-inch diameter pipe at a velocity of 6 ft/sec. When the pipe reduces to an 8-inch diameter, and all other flowing parameters remain the same, the fluid velocity becomes ________ ft/sec.
e) none of the above
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Flow in a pipe can be expressed as:
Q = A x V,
Q = volumetric flow rate, ft3/sec
A = pipe cross-sectional area, ft2
V = fluid velocity, ft/sec
The flow rate of the fluid through the 10-inch pipe (condition 1) is the same as the flow rate through the 8-inch pipe (condition 2), so:
Q1 = Q2
and since Q = A x V,
A1 x V1 = A2 x V2
Solving for V2:
V2 = A1 x V1 / A2 = [A1 / A2 ] x V1
Area is proportional to the square of the pipe diameter (A = Π x D2 / 4), so:
V2 = [(10 in)2 / (8 in)2] x 6 ft/sec
V2 = 9.375 ft/sec
The correct answer is C, 9.375 ft/sec.
Reference: Goettsche, L.D. (Editor), Maintenance of Instruments and Systems, 2nd Edition